OPTICS. 



distance of the point E of the refracted 

 ray from the perpendicular C Q, and 

 make a scale of t equal parts, of which 

 E F is one part. In like manner let us 

 take A D, the shortest distance of the 

 point A of the incident ray from the 

 same perpendicular P C, and setting it 

 upon the above scale of equal parts, we 

 shall find it to be one and one-third of 

 these parts, or, more accurately, 1.336. 

 If we now repeat this experiment when 

 the tube A G is in any other slanting 

 position, such as a C, in which case the 

 refracted ray will be C e, and making a 

 scale of equal parts, of which ef is one, 

 measure upon it the line a d, we shall 

 find that this line is also 1 .336 . Now the 

 line AD is called the sine of the angle of 

 incidence AGP, and E F the sine of the 

 angle of refraction E C Q. Hence it 

 follows, that in water the sine of the 

 angle of incidence is to the sine of the 

 angle of refraction as 1.336 to 1, what- 

 ever be the position of the ray with re- 

 spect to the surface ; that is, the Sines of 

 the angles of incidence and refraction 

 have a constant proportion or ratio to 

 one another. 



If we next fix a shining body, as a 

 sixpence, at Q, E and e in succession, 

 and place the tube successively in the 

 positions PC, AC, and a C, we shall 

 see the sixpence distinctly ; that is, when 

 the sixpence is at Q, the ray Q C pro- 

 ceeding from it, passes on to P without 

 refraction ; when the sixpence is at E, 

 the ray E C is refracted at C in the di- 

 rection C A ; and when it is at e, the 

 ray e C is refracted at C into the direc- 

 tion C a. In this case the angles E C Q, 

 e C Q are the angles of incidence, and 

 A C P, a C P, the angles of refraction, 

 and their sines E F, ef, AD, a d, being 

 the same sines which we formerly mea- 

 sured, will be to one another as 1 to 

 1.336. Hence it follows, that in refrac- 

 tions from a dense medium, such as 

 water or glass, to a rare medium, such 

 as air, the sines of the angles of inci- 

 dence and refraction have a constant 

 ratio or proportion one to another. 



By comparing these two cases of re- 

 fraction, it will be seen, that when the 

 ray A C passes from air into water, the 

 ray C E is refracted towards the per- 

 pendicular C Q, and the sine of the angle 

 of refraction is 1 , while the sine of the 

 angle of incidence is 1.336 ; but that 

 when the ray E C passes from water 

 into air, the ray C A is refracted from 

 the perpendicular CP; and the sine 

 Of the angle of incidence is 1, while 



the sine of the angle of refraction is 

 1.336. 



We are now in a situation to deter- 

 mine the direction of any ray after it is 

 refracted by the surface of water. Let 

 it be required, for example, to find the 

 direction of the ray aC,fig. 2, when it 

 is refracted after falling on the surface 

 RS of water, at the point C. Draw 

 C P perpendicular to R S, and from a 

 draw a d perpendicular to C P. Take 

 a d in the compasses, and make a scale 

 in which this distance occupies 1.336, 

 or 1 3 parts nearly ; then taking one of 

 these parts in the compasses, place one 

 foot in the circle P R Q S, described 

 round C, and passing through a, some- 

 where about m in the line a G continued, 

 and move that foot towards Q, to e for 

 example, till the other foot strikes a 

 point f in the perpendicular C Q, and 

 no other point in it, then e is the point 

 through which the refracted ray will 

 pass, and consequently the line C e must 

 be the refracted ray required. 



The number 1.336, which regulates 

 the refraction of water, is called its 

 index, or exponent, or co-efficient of 

 refraction, and sometimes its refractive 

 power. 



If we now repeat all the above expe- 

 riments with other fluids and solids, we 

 shall find, that the same law of refrac- 

 tion takes place with all of them, and 

 that ,the index of refraction, or the re- 

 fractive power, varies in each. But the 

 refractive power of bodies may be mea- 

 sured more accurately, as we shall 

 afterwards see, by different methods. 



The following TABLE contains the 

 index of refraction for a great number 

 of bodies, as determined by different 

 observers, and by different methods ; 

 and it is obvious, that by means of 

 the numbers here given, we can, in 

 the way already described, trace the 

 passage of a ray through any plain 

 surfaces by which the body may be 

 bounded. 



TABLE OF REFRACTIVE POWERS. 



Index of ' 

 Retraction. 



Chromate of lead, (greatest refr.) . 2.974 



Ruby silver , 2.5C4 



Realgar artifical 2 . 549 



Chromate of lead, (least ret'r.) .... 2 . 500 



Octohedrite 2.500 



Diamond, Rochon 2.755 



Ditto Newton 2.439 



Blende 2.260 



Phosphorus 2.224 



Glass of Antimony 2.200 



